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We propose a random coordinate descent algorithm for optimizing a non-convexobjective function subject to one linear constraint and simple bounds on thevariables. Although it is common use to update only two random coordinatessimultaneously in each iteration of a coordinate descent algorithm, ouralgorithm allows updating arbitrary number of coordinates. We provide a proofof convergence of the algorithm. The convergence rate of the algorithm improveswhen we update more coordinates per iteration. Numerical experiments on largescale instances of different optimization problems show the benefit of updatingmany coordinates simultaneously.

On convergence of a $q$-random coordinate constrained algorithm for non-convex problems